Method and apparatus for radiance capture by multiplexing in the frequency domain

ABSTRACT

An external mask-based radiance camera may be based on an external, non-refractive mask located in front of the main camera lens. The mask modulates, but does not refract, light. The camera multiplexes radiance in the frequency domain by optically mixing different spatial and angular frequency components of light. The mask may, for example, be a mesh of opaque linear elements, which collectively form a grid, an opaque medium with transparent openings, such as circles, or a pinhole mask. Other types of masks may be used. Light may be modulated by the mask and received at the main lens of a camera. The main lens may be focused on a plane between the mask and the main lens. The received light is refracted by the main lens onto a photosensor of the camera. The photosensor may capture the received light to generate a radiance image of the scene.

PRIORITY INFORMATION

This application is a divisional of U.S. application Ser. No.12/186,396, filed Aug. 5, 2008 now U.S. Pat. No. 8,019,215, which claimsbenefit of priority of U.S. Provisional Application Ser. No. 60/954,238,filed Aug. 6, 2007, the content of which is incorporated by referenceherein in their entirety.

BACKGROUND Description of the Related Art

Conventional cameras fail to capture a large amount of opticalinformation. In particular, a conventional camera does not captureinformation about the location on the aperture where different lightrays enter the camera. During operation, a conventional digital cameracaptures a two-dimensional (2-D) image representing a total amount oflight that strikes each point on a photosensor within the camera.However, this 2-D image contains no information about the directionaldistribution of the light that strikes the photosensor. Directionalinformation at the pixels corresponds to locational information at theaperture.

Light-Field or Radiance Photography

In contrast to conventional cameras, light-field, or radiance, camerassample the four-dimensional (4-D) optical phase space, or radiance, andin doing so capture information about the directional distribution ofthe light rays. This information captured by radiance cameras may bereferred to as the light-field, the plenoptic function, or radiance. Incomputational photography, radiance is a four-dimensional (4-D) recordof all light rays in 3-D. Radiance describes both spatial and angularinformation, and is defined as density of energy per unit of area perunit of stereo angle (in radians). A radiance camera captures radiance;therefore, radiance images originally taken out-of-focus may berefocused, noise may be reduced, viewpoints may be changed, and otherradiance effects may be achieved.

Conventional cameras, based on 2-D image sensors, are simply integrationdevices. In a typical setting, conventional cameras integrate over a 2-Daperture to produce a 2-D projection of the four-dimensional (4-D)radiance. Integral, or light-field, photography was proposed more than acentury ago to “undo” the integration and measure the complete 4-Dradiance arriving at all points on a film plane or photosensor. Thus,integral photography captures radiance as opposed to capturing a flat2-D picture. The light itself, or radiance, may be mathematicallydescribed by the radiance density function, which is a completerepresentation of light energy flowing along “all rays” in 3-D space.This density is a field defined in the 4-D domain of the optical phasespace, the space of all lines in 3-D with symplectic structure.Capturing the additional two dimensions of radiance data allows the raysof light to be re-sorted in order to synthesize new photographs, whichmay be referred to as novel views. Advantages of radiance photographyinclude gaining information about the 3-D structure of the scene as wellas the ability of optical manipulation or editing of the images, such asrefocusing and novel view synthesis.

Radiance may be captured with a conventional camera. In one conventionalmethod, M×N images of a scene are captured from different positions witha conventional camera. If, for example, 8×8 images are captured from 64different positions, 64 images are produced. The pixel from eachposition (i, j) in each image are taken and placed into blocks, togenerate 64 blocks.

FIG. 1 a illustrates an exemplary prior art light-field camera, orcamera array, which employs an array of two or more objective lenses110. Each objective lens focuses on a particular region of photosensor108, or alternatively on a separate photosensor 108. This light-fieldcamera 100 may be viewed as a combination of two or more conventionalcameras that each simultaneously records an image of a subject on aparticular region of photosensor 108 or alternatively on a particularphotosensor 108. The captured images may then be combined to form oneimage.

FIG. 1 b illustrates an exemplary prior art integral camera, orplenoptic camera, another type of light-field camera, which employs asingle objective lens and a microlens or lenslet array 106 thatincludes, for example, about 100,000 lenslets. Lenslet array 106 istypically placed a small distance (˜0.5 mm) from a photosensor 108, e.g.a charge-coupled device (CCD). The raw image captured with a plenopticcamera 102 is made up of an array of small images, typically circular,of the main camera lens 108. These small images may be referred to asmicroimages. The lenslet array 106 enables the plenoptic camera 102 tocapture the radiance, i.e. to record not only image intensity, but alsothe distribution of intensity in different directions at each point.Each lenslet splits a beam coming to it from the main lens 104 into rayscoming from different “pinhole” locations on the aperture of the mainlens 108. Each of these rays is recorded as a pixel on photosensor 108,and the pixels under each lenslet collectively form an n-pixel image.This n-pixel area under each lenslet may be referred to as a macropixel,and the camera 102 generates a microimage at each macropixel. Theplenoptic photograph captured by a camera 102 with, for example, 100,000lenslets will contain 100,000 macropixels, and thus generate 100,000microimages of a subject. Each macropixel contains different angularsamples of the light rays coming to a given microlens. Each macropixelcontributes to only one pixel in the different angular views of thescene. As a result, each angular view contains 100,000 pixels.

Another type of light-field camera is somewhat similar to the plenopticcamera of FIG. 1 b, except that an array of pinholes is used between themain lens and the photosensor instead of an array of lenslets.

Yet another type of light-field camera is similar to the plenopticcamera of FIG. 1 b, except that a non-refractive cosine mask is usedbetween the main lens and the photosensor instead of an array oflenslets. The cosine mask is a non-refractive element, and modulates theincoming light rays but does not refract the light. The captured imageis the convolution of the incoming light field with the mask lightfield. This camera design captures the 4-D light field directly in theFourier domain. Thus, a 2-D sensor pixel represents a coded linearcombination of several rays. The linear combination can be decoded bysoftware to obtain the 4-D light field.

Frequency Domain Analysis of Radiance

Techniques for analyzing radiance in the frequency domain have beendeveloped, among which are application of Poisson summation formula todepth representation of scenes, light fields and displays, lighttransport and optical transforms, Fourier slice theorem applied torefocusing, and others. However, frequency domain analysis has not beenapplied directly to the understanding and design of light-field, orradiance, cameras in general. Moreover, frequency domain processing hasbeen limited to mask-based radiance cameras that employ sinusoidal(e.g., cosine) masks.

SUMMARY

Various embodiments of a mask-based radiance camera are described thatmultiplex radiance in the frequency domain by optically mixing differentspatial and angular frequency components of the light received from ascene, and capture the radiance information at a photosensor.Embodiments of a mask-based radiance camera based on an external,non-refractive mask located in front of the main or objective cameralens, rather than between the main lens and the photosensor or film, aredescribed. In addition, an internal mask-based camera based on a medium-or large-format conventional camera with a film back, and anon-refractive mask that may be placed in the film back adjacent to thefilm, with optional spacers that may be placed between the mask and thefilm, is described. While both types of mask-based cameras employperiodic masks, neither is limited to sinusoidal (i.e., cosine) masks.

Various exemplary embodiments of non-refractive masks are described. Themasks are non-refractive; that is, while the masks may act to modulateand/or attenuate the light, the masks do not act to bend the light rays.An exemplary embodiment is a mesh mask, which also may be referred to asa net or screen. The mesh may include horizontally and verticallyarranged opaque linear elements or grid lines, which collectively form agrid that modulates, but does not refract, light received from a scenelocated in front of the camera as the received light passes through thegrid. Generally, the opaque grid lines may be equally spaced in the twodimensions. Thus, the opaque grid lines act to form or define rows andcolumns of periodically spaced transparent (i.e., through which lightmay pass), non-refractive openings.

Another exemplary embodiment of a mask includes transparent circularopenings, through which light may pass, in an opaque medium or surface.The circular openings in may be periodically spaced, and arranged inhorizontal rows and vertical columns. Other geometric shapes thancircles may be used in other embodiments, e.g. squares, hexagons,rectangles, etc. Another exemplary mask is composed of a grid or arrayof pinholes, and may be referred to as a pinhole mask. The pinholes,which also may be referred to as openings, may typically be, but are notnecessarily, circular. The pinholes may be periodically spaced, andarranged in horizontal rows and vertical columns.

While various examples of masks are described, in general, any ofvarious types of periodic masks may be used as a non-refractive mask inembodiments. In addition, while the masks are described as periodic, theperiodicity may be arbitrary. In other words, the masks that may be usedin embodiments of an external mask-based radiance camera are not limitedto sinusoidal masks such as sine masks and/or cosine masks. The variousembodiments of masks may be used with either the external mask-basedradiance camera embodiments or the internal mask-based radiance cameraembodiments with appropriate physical configuration to match theparticular camera application.

Various types of cameras may be used in embodiments of the externalmask-based radiance camera, including both film-based and digitalcameras, and standard, medium or large-format cameras. A non-refractivemask may be integrated with the camera, or alternatively attachable tothe camera, with the mask positioned in front of the main lens so thatlight from a scene to be photographed arrives at the main lens afterpassing through and being modulated by the mask. The mask is anon-refractive element, and modulates and/or attenuates the incominglight rays but does not bend the rays. In one embodiment, the main lensmay be focused on a plane just behind the mask, between the mask and themain lens. Light is refracted by the main lens onto a photosensor, whichmay in turn operate to capture a radiance image of the scene.

In one embodiment of a method of capturing a radiance image with anexternal mask-based radiance camera, light from a scene may be receivedat a mask. The mask is a non-refractive element, and modulates and/orattenuates the incoming light rays but does not bend them. Light thatpasses through the mask is received at the main lens of a camera. Themain lens may be focused on a plane between the mask and the main lens,and proximate to the mask. The received light is refracted by the mainlens onto a photosensor of the camera. The photosensor may capture thereceived light to generate a radiance image of the scene. In someembodiments of the camera, the captured radiance image may be stored toa memory medium or memory device.

Embodiments of an internal mask-based radiance camera based on a medium-or large-format film camera with a film back. In one embodiment, amechanism inside the film back of the film camera holds the mask so thata flat side of the mask is pressed against the film and the surface ofmask on which the opaque surface or medium is painted, attached, etc.,with openings that are the transparent portion of the mask is away fromthe film. In one embodiment, the thickness of the mask is such that,when placed against the film, the opaque surface of the mask, and theopenings therein, is at a distance f (equivalent to the focal length ofthe mask) from the film. In one embodiment, spacers may be used betweenthe mask and the film in film holder to increase the distance from themask and the film to allow f (equivalent to the focal length of themask) to be changed, for example to match a changed F/number for themain lens. Additional spacers may be added to provide additionalspacing.

The angular information of radiance images captured with embodiments ofan external mask-based radiance camera or with embodiments of aninternal mask-based radiance camera may be demultiplexed using anembodiment of a frequency domain demultiplexing method described hereinto generate multiple views of a scene. If the radiance was captured tofilm, the radiance image may be digitized from the film, for exampleusing a film negative or photograph scanner, to generate a digitalversion of the radiance image that may be stored to a memory mediumand/or processed by the frequency domain demultiplexing method.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 a illustrates an exemplary prior art light-field camera, orcamera array.

FIG. 1 b illustrates an exemplary prior art plenoptic camera.

FIG. 2 a illustrates the geometric representation of a ray as positionand angle in an optical system.

FIG. 2 b illustrates the same ray as in FIG. 2 b, but described as apoint, or a vector, in a 2-D space.

FIG. 3 illustrates a light-field camera employing an array of pinholes.

FIG. 4 a illustrates, in the frequency domain, a band-limited signalafter the array of pinholes.

FIG. 4 b illustrates the shear of the signal after traveling a distancef.

FIGS. 4 c and 4 d illustrate reconstructing the original signal beforethe array of pinholes by combining samples at different intersectionswith the ω_(q) axis.

FIG. 5 a illustrates an exemplary image obtained from a lens-basedradiance camera.

FIG. 5 b illustrates a zoom-in of a region of the image illustrated inFIG. 5 a.

FIG. 5 c illustrates the magnitude of the 2-D Fourier transforms of theimage illustrated in FIG. 5 a.

FIG. 6 a illustrates an exemplary image obtained from a mask-basedradiance camera.

FIG. 6 b illustrates a zoom-in of a region of the image illustrated inFIG. 6 a.

FIG. 6 c illustrates the magnitude of the 2-D Fourier transforms of theimage illustrated in FIG. 6 a.

FIG. 7 a illustrates an exemplary image obtained from an externalmask-based radiance camera.

FIG. 7 b illustrates a zoom-in of a region of the image illustrated inFIG. 7 a.

FIG. 7 c illustrates the magnitude of the 2-D Fourier transforms of theimage illustrated in FIG. 7 a.

FIG. 8 illustrates a method of demultiplexing the angular information ofan image captured using a radiance camera, according to one embodiment.

FIGS. 9 a and 9 b illustrate a method of correcting the effect of wavesdue to small shifts or misalignments in the FFT, according to oneembodiment.

FIG. 10 illustrates a frequency domain demultiplexing module, accordingto one embodiment.

FIG. 11 a shows an exemplary radiance image captured with a lens-basedradiance camera.

FIG. 11 b shows the absolute value of the Fourier transform of theradiance image of FIG. 11 a.

FIGS. 12 a and 12 b show two stereo views from the frequency domainreconstructed light field of FIGS. 11 a and 11 b.

FIG. 13 shows a conventional medium-format film camera and a film back,with a computer screen filter, used as a mask, attached to the windowjust in front of the film, according to one embodiment.

FIG. 14 shows two stereo views generated from a radiance image takenusing an exemplary mask-based radiance camera.

FIG. 15 shows a picture taken through a net, or mesh, located in frontof a conventional camera.

FIG. 16 shows two stereo views from the radiance generated from thepicture shown in FIG. 15.

FIG. 17 illustrates exemplary net- or mesh-like, non-refractive masks,according to embodiments.

FIG. 18 illustrates other exemplary non-refractive masks, according toembodiments.

FIG. 19 illustrates an exemplary radiance camera with an external maskattachment, according to one embodiment.

FIG. 20 illustrates a method of capturing a radiance image with anexternal mask-based radiance camera, according to one embodiment.

FIG. 21 illustrates an exemplary embodiment of an internal mask-basedradiance camera based on a medium- or large-format film camera with afilm back.

FIG. 22 illustrates an exemplary computer system that may be used inembodiments.

While the invention is described herein by way of example for severalembodiments and illustrative drawings, those skilled in the art willrecognize that the invention is not limited to the embodiments ordrawings described. It should be understood, that the drawings anddetailed description thereto are not intended to limit the invention tothe particular form disclosed, but on the contrary, the intention is tocover all modifications, equivalents and alternatives falling within thespirit and scope of the present invention as defined by the appendedclaims. The headings used herein are for organizational purposes onlyand are not meant to be used to limit the scope of the description orthe claims. As used throughout this application, the word “may” is usedin a permissive sense (i.e., meaning having the potential to), ratherthan the mandatory sense (i.e., meaning must). Similarly, the words“include”, “including”, and “includes” mean including, but not limitedto.

DETAILED DESCRIPTION OF EMBODIMENTS

Various embodiments of a method and apparatus for capturing radiance inthe frequency domain, and demultiplexing the captured radiance in thefrequency domain, are described. Various embodiments of light-field, orradiance, cameras, including both mask-based and lens-based radiancecameras, are described that multiplex the radiance in the frequencydomain by optically mixing different spatial and angular frequencycomponents and capturing the signal via a photosensor (e.g.,conventional film or an electronic sensor such as a charge-coupleddevice (CCD)). Some embodiments of the radiance camera may be based onarrays of “active” optical elements, such as lenses and prisms. Otherembodiments of the radiance camera may be based on “passive” opticalelements, or masks, such as meshes or grids of circles or pinholes. Bothtypes of radiance cameras may be understood and described according to amathematical formalism in the frequency domain.

In the following sections, a mathematical analysis of radiance camerasin the frequency domain is provided. A method of multiplexing the 3-Dradiance onto the 2-D sensor is demonstrated that works in the frequencydomain for various radiance cameras, including both lens-based andmask-based radiance cameras. It is also demonstrated that the F/numbermatching condition known to exist for lens-based radiance cameras is arequirement for all radiance cameras. This helps in constructing andadjusting various mask- and lens-based radiance cameras so that thecameras produce higher quality radiance images.

A mathematical method for recovering (demultiplexing) the multiplexedspatial and angular information from the frequency representation isalso described, and is shown to be applicable to radiance imagescaptured by both lens-based and mask-based radiance cameras, includingradiance images captured with mask-based cameras that employ anyperiodic mask. This method may be referred to as a frequency domaindemultiplexing method. The frequency domain demultiplexing method may,for example, be implemented in a computer software program or module,referred to herein as a frequency domain demultiplexing module.

Conventionally, frequency domain demultiplexing methods similar to thefrequency domain demultiplexing method described herein have beenlimited to radiance images captured specifically with mask-basedradiance cameras that use sinusoidal (i.e., cosine or sine) masks.Embodiments of the frequency domain demultiplexing method are describedfor which it is shown that the method may be used to demultiplexradiance information from images captured with mask-based radiancecameras that use any periodic mask, not just sinusoidal masks, and forwhich it is also shown that the method may to demultiplex radianceinformation captured with lens-based radiance cameras in addition tomask-based cameras.

In addition, embodiments of a radiance camera based on an external mask,e.g. a periodic screen, mesh or grid of openings, such as pinholes orcircles, in an opaque surface or element located in front of the maincamera lens, rather than between the main lens and the photosensor orfilm, are described. Furthermore, embodiments of a radiance camera basedon an internal periodic but non-sinusoidal mask located in between themain cameral lens and the photosensor or film, are described.

Frequency Domain Representation

Let r(x) be the radiance in conventional x-space. This can berepresented in frequency domain as follows:R(ω)=∫r(x)e ^(iω·x) dx  (1)

The following notations are used. The spatio-angular coordinates of aray at a given plane orthogonal to the optical axis are represented as avector:

$\begin{matrix}{x = \begin{pmatrix}q \\p\end{pmatrix}} & (2)\end{matrix}$where q is the location of ray-plane intersection, and p is a vectordefining the two angles of that ray at location q. Paraxialapproximation is used, assuming the angle is small. A 2-dimensionalvector representation of a ray is shown in FIGS. 2 a and 2 b. FIG. 2 aillustrates the geometric representation of a ray as position and anglein an optical system. FIG. 2B illustrates the same ray as in FIG. 2 b,but described as a point, or a vector x=(q, p), in a 2-D space.

The spatial frequency ω_(g) and the angular frequency ω_(p) may berepresented in a similar way as a 4-D vector:

$\begin{matrix}{\omega = \begin{pmatrix}\omega_{q} \\\omega_{p}\end{pmatrix}} & (3)\end{matrix}$

To simplify the description and the Figures, 2-D radiance with1-dimensional position q and angle p for each ray may be used. The dotproduct may be defined as:ω·x=ω _(q) q+ω _(p) pTransformations of the Radiance

The following summarizes and extends transformations of radiance inoptical systems. A ray x may be transformed as described below.

Both lens L and translation T may be described by linear transformsx′=A_(x) of the ray as a position-angle vector (see equation (2)) by thefollowing matrices:

$\begin{matrix}{L = \begin{pmatrix}1 & 0 \\{- \frac{1}{f}} & 1\end{pmatrix}} & (4) \\{T = \begin{pmatrix}1 & t \\0 & 1\end{pmatrix}} & (5)\end{matrix}$where f is the focal length of the lens, and t is the translation(distance of flight). A prism deviates the ray by a fixed anglep_(prism), so that p′=p+p_(prism).

The combined action of several such elements may be described by thecomposition of all those elements. This provides the ability to buildthe model of essentially any optical system, such as a multi-elementcamera lens or radiance camera, as a linear or affine transform.

In a non-absorbing optical system, the radiance is conserved. In otherwords, the radiance does not change along a ray during travel ortransformation by optical elements. The mathematical representation ofthis fact is that any optical matrix is symplectic. The followingproperty of the transforms, that the determinant of any optical matrixis 1, may be used herein:detA=1  (6)

The above may also be seen directly from equations (4) and (5).

Based on the above-mentioned conservation law that, n a non-absorbingoptical system, the radiance is conserved, the radiance r′ after atransform is related to the radiance r before the transform by thefollowing equation:r′(x)=r(x ₀)=r(A ⁻¹ x)  (7)where x₀ is the ray, which has been mapped into x by the opticaltransformation A, i.e. x=Ax₀.

Equation (7) may be expressed in frequency representation as follows:

$\begin{matrix}\begin{matrix}{{R^{\prime}(\omega)} = {\int{{r^{\prime}(x)}{\mathbb{e}}^{{\prime\omega} \cdot x}{\mathbb{d}x}}}} \\{= {\int{{r( {A^{- 1}x} )}{\mathbb{e}}^{{\prime\omega} \cdot x}{\mathbb{d}x}}}} \\{= {\int{{r( {A^{- 1}x} )}{\mathbb{e}}^{{\prime\omega}\;{AA}^{- 1}x}{\mathbb{d}x}}}} \\{= {\int{{r( x_{0} )}{\mathbb{e}}^{{\prime\omega}\;{A \cdot x_{0}}}{\mathbb{d}x_{0}}}}} \\{= {R( {A^{T}\omega} )}}\end{matrix} & (8)\end{matrix}$where A^(T) is the transposed matrix, and equation (6) is used for thechange of variables from x to x₀. Note that this expression is derivedfor any optical transform A, while conventional works have onlyconsidered the special cases.

The above results may be summarized as follows:x′=Ax  (9)r′(x)=r(A ⁻¹ x)  (10)R′(ω)=R(A ^(T)ω)  (11)Radiance Cameras in the Frequency DomainThe Pinhole Light-Field Camera

One type of radiance camera, which may be referred to as a pinholelight-field camera, may be described as an array of pinhole cameras withthe same focal distance f, as illustrated in FIG. 3. This array of“cameras” may be placed at the focal plane of a conventional camera,typically but not necessarily a large format camera. Note that, in FIG.3, only the focal plane with the array of pinholes is represented.

The mathematical representation for the radiance transformations insidea pinhole light-field camera in the frequency domain is described below.This representation may be used throughout the description.

Consider a 1-dimensional pinhole light-field camera and thecorresponding 2-D radiance. Just before the array of pinholes, theradiance is:r(x)=r(q, p)

Just after the array of pinholes, the radiance is:

$\begin{matrix}{{r^{\prime}( {q,p} )} = {{r( {q,p} )}{\sum\limits_{m = {- \infty}}^{\infty}\;{\delta( {q - {mb}} )}}}} & (1)\end{matrix}$where b is the pitch (distance between pinholes). In frequencyrepresentation this radiance may be written based on the Poissonsummation formula as:

$\begin{matrix}\begin{matrix}{{R^{\prime}(\omega)} = {\int{{r( {q,p} )}{\sum\limits_{m}^{\;}\;{{\delta( {q - {mb}} )}{\mathbb{e}}^{{\mathbb{i}\omega} \cdot x}{\mathbb{d}x}}}}}} \\{= {\frac{1}{b}{\int{{r( {q,p} )}{\sum\limits_{n}^{\;}\;{{\mathbb{e}}^{{in}\frac{2\pi\; q}{b}}{\mathbb{e}}^{{\mathbb{i}}{({{\omega_{q}q} + {\omega_{p}p}})}}{\mathbb{d}q}{\mathbb{d}p}}}}}}} \\{= {\frac{1}{b}{\sum\limits_{n}^{\;}\;{R( {{\omega_{q} + {n\frac{2\pi}{b}}},w_{p}} )}}}}\end{matrix} & (13)\end{matrix}$

Assuming a band-limited signal, this result shows that the radianceafter the pinholes consists of multiple copies of the original radiance,shifted in their frequencies by:

$n\frac{2\pi}{b}$for all integers n, as shown in FIG. 4 a, which illustrates aband-limited signal after the array of pinholes. FIG. 4 b illustratesthe shear of the signal after traveling a distance f.

After traveling a distance f from the pinholes to the image plane, theradiance is transformed by the translation matrix (5) transposed,according to equation (11). The resultant radiance R_(f) that reachesthe film plane is:

$\begin{matrix}{{R_{f}(\omega)} = {\sum\limits_{n = {- \infty}}^{\infty}\;{R( {{\omega_{q} + {n\frac{2\pi}{b}}},{{f\;\omega_{q}} + \omega_{p}}} )}}} & (14)\end{matrix}$

It can be seen that the signal is sheared in the direction of angularfrequency.

This is represented in FIG. 4 b, which illustrates the shear of thesignal after traveling a distance f. An observation is that a differentangular part of each copy intersects with the ω_(q) axis. Since the film(or sensor) responds only to the zero angular frequency, it records onlythe thin slice where the spectrum intersects with the ω_(q) axis.

By picking up slices in the image at different angular frequencies andstacking the slices along the ω_(q) axis, the original signal R(ω_(q),ω_(p)) may be reconstructed, as shown in FIGS. 4 c and 4 d whichillustrate reconstructing the original signal before the pinhole arrayby combining samples at different intersections with the ω_(q) axis.Finally, an inverse Fourier transform may be applied to convert theradiance into the familiar spatio-angular representation r(x).

From the above analysis of a pinhole light-field camera in the frequencydomain, radiance capture by multiplexing in the frequency domain may beapplied to pinhole light-field cameras. A frequency domaindemultiplexing method may be applied to the captured radiance todemultiplex the radiance information. The angular information ofradiance images captured with a pinhole light-field camera may, forexample, be demultiplexed using a frequency domain demultiplexing methodas illustrated in FIG. 8 to generate multiple parallax views of a scene.In addition, while a pinhole array is periodic, the periodicity of thepinholes in the array may be arbitrary. In other words, the pinholearrays that may be used as a mask in a pinhole light-field or radiancecamera are not limited to sinusoidal masks such as sine masks and/orcosine masks.

Replacing the Pinhole Array with a Lens Array—the Integral Camera

The pinholes in the pinhole light-field camera design may be replacedwith lenses. Just as with a single pinhole camera, lenses gather muchmore light and produce better image quality than small pinholes. Such aradiance camera may be referred to as an integral camera. Differentversions of the integral camera have been proposed, including theplenoptic camera illustrated in FIG. 1 b.

An analysis of the integral camera in frequency space may be performedaccording to the following:

-   -   An array of pinholes, as in the pinhole camera, may be        considered, only shifted by a constant (for all pinholes)        vector a. Each pinhole is covered by a prism with angle of        deviation depending on the shift, defined as

$p_{prism} = {\frac{a}{f}.}$

-   -   The superposition of multiple arrays of such pinhole-prisms may        be considered, and it may be shown that they all contribute to        the final image in the same way. A conventional integral camera        may be based on this coherent action of different arrays. Such a        camera may be viewed as the limiting case where the plane is        made completely of pinhole-prisms and all the light goes        through. Each microlens is formed by the corresponding prisms,        as a Fresnel lens.

Following the above derivation for the pinhole light-field camera inequation (13), the radiance after the pinhole-prism array may beexpressed as:

$\begin{matrix}\begin{matrix}{{R^{\prime}(\omega)} = {\int{{r( {q,{p + \frac{a}{f}}} )}{\sum\limits_{m}^{\;}\;{{\delta( {q - {mb} - a} )}{\mathbb{e}}^{{\mathbb{i}\omega} \cdot x}{\mathbb{d}x}}}}}} \\{= {\frac{1}{b}{\int{{r( {q,{p + \frac{a}{f}}} )}{\sum\limits_{n}^{\;}\;{{\mathbb{e}}^{{in}\frac{2{\pi(\;{q - a})}}{b}}{\mathbb{e}}^{{\mathbb{i}}{({{\omega_{q}q} + {\omega_{p}p}})}}{\mathbb{d}q}{\mathbb{d}p}}}}}}} \\{= {\frac{1}{b}{\sum\limits_{n}^{\;}{{\mathbb{e}}^{- {{\mathbb{i}}{({{\omega_{p}\frac{a}{f}} + {n\frac{2\pi\; a}{b}}})}}}\;{R( {{\omega_{q} + {n\frac{2\pi}{b}}},w_{p}} )}}}}}\end{matrix} & (15)\end{matrix}$

Note that additional phase multipliers are now present in each term ofthe sum. After the pinhole-prism array, the light travels a distance fto the film plane. Using equations (5) and (9), the following expressionfor the radiance at the film (sensor) may be obtained:

${R_{f}(\omega)} = {\frac{1}{b}{\sum\limits_{n}^{\;}\;{{\mathbb{e}}^{- {{\mathbb{i}}{({{{({{f\;\omega_{q}} + \omega_{p}})}\frac{a}{f}} + {n\frac{2\pi\; a}{b}}})}}}{R( {{\omega_{q} + {n\frac{2\pi}{b}}},{{f\;\omega_{q}} + \omega_{p}}} )}}}}$

As explained above, the film (or sensor) only records zero angularfrequencies. Therefore, by restricting ω to the ω_(q) axis, thefollowing expression may be obtained:

$\begin{matrix}{{R_{f}( {\omega_{q},0} )} = {\frac{1}{b}{\sum\limits_{n}^{\;}\;{{\mathbb{e}}^{- {{\mathbb{i}}{({{\omega_{q}a} + {n\frac{2\pi\; a}{b}}})}}}{R( {{\omega_{q} + {n\frac{2\pi}{b}}},{f\;\omega_{q}}} )}}}}} & (16)\end{matrix}$

An effect of coherence may be easily observed for a small a. It takesplace due to the term:

${\omega_{q}a} + {n\frac{2\pi\; a}{b}}$where ω_(q) is within

$\frac{\pi}{b}$from the corresponding center (peak), which is at frequency

$n\frac{2\pi}{b}$in each block. For every exponential term with frequency ω_(q), there isanother term with frequency:

${{- n}\frac{2\pi}{b}} - \omega_{q}$inside the same block, but on the other side of the center. Those twofrequencies produce opposite phases, which results in a real positiveterm:

$\cos( {( {\omega_{q} + {n\frac{2\pi}{b}}} )a} )$This term for a small a is close to 1 for all rays.Based on this analysis, the integral camera will also work with lensesfor which a can be as big as

$\frac{b}{2}$and the area of the plane is completely covered. All the terms are stillpositive, but the efficiency of rays far from the center is lower, andhigh frequencies will be attenuated.

The above analysis proves that the frequency method for multiplexingradiance, described in the case of the pinhole light-field camera, isalso valid for a microlens-based integral camera. Similarly, theplenoptic camera, e.g. as illustrated in FIG. 1 b, and other lens-basedradiance cameras that may be shown equivalent to it, can be analyzedusing this formulation.

From the above analysis, radiance capture by multiplexing in thefrequency domain may be applied to lens-based radiance cameras ingeneral. It follows that a frequency domain demultiplexing method may beapplied to the radiance captured by a lens-based radiance camera todemultiplex the radiance information. The angular information ofradiance images captured with a lens-based radiance camera may, forexample, be demultiplexed using a frequency domain demultiplexing methodas illustrated in FIG. 8 to generate multiple parallax views of a scene.

Replacing the Pinhole Array with a Mask

Radiance cameras that use a periodic sinusoidal mask (e.g., a cosinemask) instead of pinholes or microlenses between the photosensor and themain lens of the camera, and proximate to the photosensor, have beenproposed. One way to analyze these mask-based radiance cameras would beto start again with the pinhole formula derived for the pinholelight-field camera, and instead of prisms assume appropriate attenuationat each pinhole. On the other hand, it is also possible to directlyderive the result for periodic attenuation functions, such as:

$\frac{1}{2}( {1 + {\cos( {\omega_{0}q} )}} )$

The radiance after the attenuating mask may be represented as:

$\begin{matrix}\begin{matrix}{{R^{\prime}(\omega)} = {{\frac{1}{2}{R(\omega)}} + {\frac{1}{2}{\int{{r(x)}{\cos( {\omega_{0}q} )}{\mathbb{e}}^{{\mathbb{i}\omega} \cdot x}{\mathbb{d}x}}}}}} \\{= {{\frac{1}{2}{R(\omega)}} + {\frac{1}{4}{\int{{r(x)}( {{\mathbb{e}}^{{\mathbb{i}\omega}_{0}q} + {\mathbb{e}}^{{- {\mathbb{i}\omega}_{0}}q}} ){\mathbb{e}}^{{\mathbb{i}\omega} \cdot x}{\mathbb{d}x}}}}}} \\{= {{\frac{1}{2}{R(\omega)}} + {\frac{1}{4}( {{R( {{\omega_{q} + \omega_{0}},\omega_{p}} )} + {R( {{\omega_{q} - \omega_{0}},\omega_{p}} )}} )}}}\end{matrix} & (17)\end{matrix}$

After the mask, the signal travels a distance f to the sensor. Againusing equations (5) and (11) the following expression for the radiancemay be obtained:

$\begin{matrix}{{R_{f}( {\omega_{q},\omega_{p}} )} = {{\frac{1}{2}{R( {\omega_{q},{{f\;\omega_{q}} + \omega_{p}}} )}} + {\frac{1}{4}( {{R( {{\omega_{q} + \omega_{0}},{{f\;\omega_{q}} + \omega_{p}}} )} + {R( {{\omega_{q} - \omega_{0}},{{f\;\omega_{q}} + \omega_{p}}} )}} )}}} & (18)\end{matrix}$

Again, duplication of the band-limited signal into multiple blocks andshearing proportional to the travel distance may be observed. It isimportant to note that any periodic mask, not just sinusoidal masks suchas cosine masks, may be analyzed this way based on Fourier seriesexpansion and considering individual component frequencies. Samples ofthe signal on the ω_(q) axis may be used to reconstruct the completeradiance R(ω).

Placing the Array in Front of the Camera

Another type of radiance camera may be implemented by placing any one ofthe optical elements or arrays (mask, microlens array, pinhole array)described as internal elements in relation to the various radiancecamera designs in front of the main lens of a conventional camerainstead of inside the camera between the photosensor and the main lens,and focusing the camera slightly behind the array. This external arrayradiance camera design is possible based on the fact that the imageinside any camera is 3-dimensional, and is a distorted copy of theoutside world. It is clear that the structures placed inside the camerahave corresponding structures in the outside world. This is based on themapping defined by the main camera lens.

The photosensor plane corresponds to the plane of focus, and any opticalelements in front of the photosensor plane may be replaced by theirenlarged copies in the real world, in front of the external plane offocus. Because of this correspondence, and based on the lens formula,optical elements may be built or placed in front of the camera and usedas if they were microstructures inside the camera. Later in thisdocument, in the section titled External mask-based radiance camera, adiscussion is provided that is directed at replacing a fine mask orscreen in front of the photosensor or film, in an area not accessibledue to the cover glass, with a non-refractive mask, e.g. a net, mesh orscreen, in front of the camera, and embodiments of an externalmask-based radiance camera based on this notion are described.

Matching the F/Numbers

For lens-based radiance cameras that employ an array of microlensesinside the camera, such as the plenoptic camera illustrated in FIG. 1 b,there exists a restriction that the F/numbers of the main camera lensand the microlenses should be matched. This restriction is based on thefollowing characteristics of or observations about such cameras. Ifdensely packed microlenses in a radiance camera had a smaller F/numberthan the main (objective) lens, then parts of the images of the mainlens would extend beyond the area covered by the correspondingmicrolens, and would interfere with the images refracted by theneighboring microlens, and vice versa. If the F/number of themicrolenses were bigger, then part of the area of the photosensor undereach microlens would not be used. Thus, to maximize usage of thephotosensor and to minimize interference, the F/number of themicrolenses should match the F/number of the main or objective lens in alens-based radiance camera.

Thus, a photographer is not free to change the aperture of the maincamera lens without considering the current aperture of the microlensesin a lens-based radiance camera. Whether this restriction is relaxed inany way for other radiance cameras that are not based on microlenses,and whether there exists a quantity equivalent to F/number in casesother than microlenses, are questions that may be addressed viafrequency domain analysis of radiance cameras.

The final expression for the radiance in all radiance cameras has asecond (angular frequency) argument in R equal to fω_(q), where fis thedistance from the pinholes, microlenses or mask to the photosensor. Thisis a measure for the amount of shear, which can be seen as the tilt ofthe line fω_(q) in FIG. 4 b. Assume a radiance camera is sampling theangular frequency N times, i.e., copies of the signal that intersectwith the ω_(q) axis N times. For example, this could be a maskcontaining N frequencies at interval ω₀, or N peaks, including the zerofrequency peak. The frequency spectrum of this signal covers an intervalof Nω₀ in the horizontal axis. Because of the tilt, those peaks arespread in the vertical ω_(p) axis in an interval of Nω₀. Therefore, thefollowing expression holds:2ω_(p0) =fNω ₀  (19)where ωp₀ is the maximal angular frequency of the original signal. Thewidth of the cone of rays (maximal angle of rays) coming to a point onthe film plane in a camera is

$\frac{1}{F},$where F is the F/number of the main lens. If the maximal resolution(number of lines) in a radiance camera in an angular direction is N,then the maximal angular frequency would be ω₀=2πNF. By substituting inequation (19), the following equation may be obtained:fω ₀=4πF  (20)

Since the wavelength is b, so that

${\omega_{0} = \frac{2\pi}{b}},$the following equation may be obtained:

$\begin{matrix}{{f\frac{2\pi}{b}} = {4\pi\; F}} & (21)\end{matrix}$

The maximal spatial frequency in the initial band-limited spectrum is

$\frac{\omega_{0}}{2},$and the signal has wavelength 2 b. In this way, the following equationmay be obtained:

$\begin{matrix}{\frac{f}{b} = F} & (22)\end{matrix}$

Thus, all radiance cameras multiplexing in the frequency domain shouldsatisfy the F/number matching condition of equation (22), where F is theF/number of the objective lens, b is the pitch of the pinholes ormicrolenses, or the period of the lowest frequency in the mask, and f isthe distance from the outer surface of the mask or array of pinholes ormicrolenses (the surface closest to the objective lens) to the sensorfor internal mask, pinhole array, and microlens radiance cameras. Forexternal equivalents to internal radiance cameras, such as the externalmask-based camera 300 illustrated in FIG. 19, f is the distance from theexternal mask to the plane at which the main lens is focused behind themask.

Demultiplexing in the Frequency Domain

The method of frequency domain analysis has been applied in the sectionsabove to the images captured by the various radiance camera designs. Inthis section, methods of demultiplexing in the frequency domain torender images from radiance captured by the different radiance cameradesigns is described, and examples from each of the various radiancecamera designs are shown.

Methods of Demultiplexing

In all of the aforementioned radiance camera designs, the 4-dimensionalradiance is multiplexed onto the 2-dimensional camera sensor or film.This process of radiance multiplexing is given by equations (14), (16)and (18) for the respective camera designs. It is noted that the entire4-D light field is encoded in a radiance image captured with a radiancecamera.

FIGS. 5 a, 6 a, and 7 a illustrate exemplary images obtained from thethree aforementioned radiance camera designs. FIG. 5 a illustrates anexemplary image obtained from a lens-based radiance, or integral,camera. FIG. 6 a illustrates an exemplary image obtained from amask-based radiance camera in which the mask is located internal to thecamera between the photosensor and the main lens. FIG. 7 a illustratesan exemplary image obtained from an external mask-based radiance camera,such as camera 300 of FIG. 19, in which a net or mesh is placed in frontof the main lens of a conventional camera. FIGS. 5 b, 6 b, and 7 billustrate a zoom-in of a region of the images illustrated in FIGS. 5 a,6 a, and 7 a, respectively, and show more detail. FIGS. 5 c, 6 c, and 7c illustrate the magnitudes of the 2-D Fourier transforms of the imagesillustrated in FIGS. 5 a, 6 a, and 7 a, respectively. The shifted slicesor tiles of the transform are visible in each of the images shown inFIGS. 5 c, 6 c, and 7 c. Notice that these slices or tiles are placed atequal distances both horizontally and vertically in the case of thelens-based radiance camera image of FIGS. 5 a-5 c and externalmask-based radiance camera image of FIGS. 7 a-7 c, and only horizontallyin the case of the mask-based radiance camera images of FIGS. 6 a-6 c.This is due to the use of a mask consisting of only vertical lines inthe mask-based radiance camera (see FIG. 6 b). In all three cases,examples will be shown of extracting horizontal parallax, but it isnoted that extending the method to obtain parallax in both directions isstraightforward.

There exist several conventional techniques that may be used to extractindividual parallax views from a radiance image. Frequency domainmultiplexing techniques have been described for radiance images capturedwith conventional mask-based radiance cameras that specifically usecosine masks, and a frequency domain demultiplexing method may beapplied to these radiance images. In the case of lens-based radiancecameras, spatial multiplexing techniques as opposed to frequency domainmultiplexing techniques are conventionally used. In an exemplary spatialmultiplexing technique, pixels belonging to each “little camera” of aradiance camera (e.g., to each microlens in a microlens array) may beextracted from the captured image, rearranged and put into individualimages, so that a 2-D array of 2-D images is obtained. However, thefrequency domain analysis of various radiance cameras provided above hasshown that frequency domain multiplexing can be applied to lens-basedradiance cameras and to pinhole light-field cameras in addition tomask-based radiance cameras, to external mask-based radiance cameras,and to mask-based cameras with masks that are not necessarily sinusoidalmasks. It follows that a frequency domain demultiplexing method, such asthe one described below, may be applied to radiance images captured withother types of radiance cameras than conventional cosine mask-basedradiance cameras.

FIG. 8 illustrates a method of demultiplexing the angular information ofa radiance image captured using a radiance camera, according to oneembodiment. The Figure shows an exemplary application of a frequencydomain demultiplexing method to the radiance image illustrated in FIG. 6a, which was captured using an internal mask-based radiance camera, butit is noted that the same or a similar method may be applied to radianceimages captured with the other types of radiance cameras, including butnot limited to lens-based radiance cameras and external mask-basedradiance cameras.

The frequency domain demultiplexing method illustrated in FIG. 8 may bebased on the separability of the Fourier transform 200 of the originalcaptured radiance image. Depending on the configuration of the opticalelements in the radiance camera (whether lens-based or mask-based),three or four dimensions may be multiplexed in the radiance, with twospatial and one or two angular dimensions. For example, a radiance imagecaptured using a mask 302C of FIG. 17 may include only one angulardimension, while a radiance image captured with a mask 302A of FIG. 17may include two angular dimensions. With reference to FIGS. 4 a through4 d, the slices or tiles 204 of the 2-D Fourier transform 200 may beextracted, as indicated at 202. As indicated at 206, a 2-D inverseFourier transform (IFFT) is individually applied to each of the slicesto obtain intermediate images 208. As indicated at 210, the intermediateimages 208 are stacked together to form a 3-D image or a 4-D image 212,depending on the number of angular dimensions in the radiance. Finalhorizontal parallax images 216 may be obtained by applying a 1-D or 2-Dinverse Fourier transform (IFFT) along the angular dimension of the 3-Dimage or along the two angular dimensions of the 4-D image andunstacking the results, as indicated at 214. This process is effectivelyperforming a 3-D IFFT. In the general case of horizontal and verticalparallax, the process is extended to 4-D IFFT. Again, FIG. 8 is directedat extracting horizontal parallax, but it is noted that extending themethod to obtain parallax in both horizontal and vertical directions isstraightforward. In one embodiment, an extension of the method toextract vertical parallax may apply the same or similar elements 202,206, 210 and 214 on the vertical axis of the Fourier transform, e.g. theimages shown in FIGS. 5 c and 7 c, of the radiance image.

FIGS. 9 a and 9 b illustrate a method of correcting the effect of wavesdue to small shifts or misalignments in the FFT, according to oneembodiment. Good artifact-free results are very sensitive to determiningthe location of the centers of the slices or tiles in the Fouriertransforms. The Fourier transforms of the images may be obtained by FastFourier Transform, which makes the location of the centers of the slicesambiguous due to the discretization. There may be a misplacement errorwithin one pixel around each center, which may cause low-frequency wavesin the final parallax images. In one embodiment, this problem may beaddressed by multiplying the images before the last 1-D IFFT by a linearphase that corresponds to the subpixel shift in the FFT to morecorrectly determine the centers of the slices. FIG. 9 a shows an imagefrom a mask-based radiance camera before the phase correction is appliedto eliminate the low-frequency waves, and FIG. 9 b shows the image afterthe phase correction is applied to eliminate the low-frequency waves.

Embodiments of the frequency domain demultiplexing method describedabove may be implemented in software as or in one or more frequencydomain demultiplexing modules. The module(s) may, for example, beimplemented in a radiance image processing application or library. FIG.22 illustrates an exemplary computer system in which embodiments of thefrequency domain demultiplexing module may be implemented.

FIG. 10 illustrates a frequency domain demultiplexing module, accordingto one embodiment. Radiance image 410 may be captured with any of avariety of radiance cameras, including but not limited to variouslens-based radiance cameras, internal mask-based radiance cameras,external mask-based radiance cameras, internal and external mask-basedradiance cameras that use periodic masks that are not necessarilysinusoidal (e.g., cosine) masks, radiance cameras that use an internalor external net, screen or mesh as a mask rather than a conventionalmask, and pinhole light-field cameras. Frequency domain demultiplexingmodule 400 obtains or receives an input radiance image 410. Frequencydomain demultiplexing module 400 performs a frequency domaindemultiplexing method, for example as described in FIG. 8, on the inputimage 410 to generate multiple output images 440, for example multipleparallax views of a scene for which the radiance information wascaptured in radiance image 410. In one embodiment, during the method,the method of correcting the effect of waves due to small shifts ormisalignments in the FFT, as described above in reference to FIGS. 9 aand 9 b, may be applied. Output images 440 may, for example, be storedto a storage medium 450, such as system memory, a disk drive, DVD, CD,etc.

In one embodiment, frequency domain demultiplexing module 400 mayprovide a user interface that provides one or more textual and/orgraphical user interface elements, modes or techniques via which a usermay view or control various aspects of frequency domain demultiplexing.For example, the user interface may include user interface elements thatallow a user to select input and output files, to specify opticalcharacteristics of the radiance camera used to capture the inputradiance image, and so on.

Radiance Camera Embodiments

Embodiments of the frequency domain demultiplexing method of FIG. 8 maybe applied to radiance images captured with various types of radiancecameras, including but not limited to lens-based radiance cameras andmask-based radiance cameras. Several embodiments of different types ofradiance cameras are described below.

Lens-Based Radiance Cameras

Embodiments of the frequency domain demultiplexing method of FIG. 8 maybe applied to radiance images captured with lens-based radiance cameras,for example radiance images captured with a plenoptic camera such asplenoptic camera 102 illustrated in FIG. 1 b. To illustrate thefrequency domain demultiplexing method of FIG. 8 for a lens-basedcamera, a simulation of the plenoptic/integral camera may beaccomplished by taking multiple images of a scene with one conventionallens camera. For example, as a simulation of the plenoptic/integralcamera, 49 images of a scene may be taken from equally spaced locations.The centers of projection may be arranged on a plane as a 7×7 grid, withthe cameras pointed perpendicular to the plane. The final image is madeup of 7-pixel×7-pixel blocks, each of which consists of 49 pixels takenfrom the same location in all 49 images. FIG. 11 a shows an exemplaryradiance image taken using the above apparatus. Zoomed area 250 showsthe formed blocks. FIG. 11 b shows the absolute value of the Fouriertransform of the radiance image of FIG. 11 a. To obtain horizontalparallax, the frequency domain demultiplexing method of FIG. 8 may beapplied, with 7 views. Two images resulting from this process are shownin FIGS. 12 a and 12 b, which show two stereo views from the frequencydomain reconstructed light field of FIGS. 11 a and 11 b. Small parallaxis visible in this stereo pair at close examination. Note that the leftand right images are switched. The left and right images are switched sothat stereo fusion can be achieved with crossed eyes observation. Notethat the embodiments of lens-based radiance cameras described herein areexemplary, and not intended to be limiting. Other embodiments oflens-based radiance cameras, using various types of film-based ordigital camera designs, are possible and contemplated.

Mask-Based Radiance Camera Implementations

Embodiments of the frequency domain demultiplexing method of FIG. 8 maybe applied to radiance images captured with non-refractive mask-basedradiance cameras. Various different mask-based radiance camera designsare described that may be used to illustrate the frequency domaindemultiplexing method of FIG. 8 for images captured with a mask-basedradiance camera. In order to achieve good resolution, a small value ofthe largest period b, on the order of 0.1 mm, may be used. With F/numberof the main lens equal to 4, the mask may be placed about 0.4 mm fromthe surface of the sensor, which may not be possible due to the coverglass. Because of the cover glass restriction, embodiments of amask-based radiance camera based on a film-based, medium format cameramay be used. Reasons for using a medium format camera may include thelarger image that gives potential for higher resolution and easieraccess to the film back, where modifications may be made to convert theconventional camera into a mask-based radiance camera. The embodimentsof mask-based radiance cameras described herein are exemplary, and notintended to be limiting. Other embodiments using other types offilm-based or digital camera designs and/or other types of masks arepossible and contemplated.

In an exemplary embodiment of a mask-based radiance camera, a Contax™645 medium format film camera with a film back may be used (see FIG.13). Note that various other film cameras with film backs could besubstituted for the Contax™ camera. Exemplary embodiments that usedifferent mesh, net or screen masks are described. Refer to FIG. 17 forexemplary net- or mesh-like non-refractive masks.

In a first exemplary embodiment, a picture of a poster displaying acomputer-generated grid is taken, and then the negative is used as amask in front of the film in the film back. In one embodiment, thecomputer-generated grid is a 2-D cosine mask with 3 harmonics in bothspatial dimensions. The spacing of 0.5 mm may be achieved by placing thedeveloped negative between two thin glasses to form a non-refractivemask. The film that is being exposed slides directly on the surface ofthe glass.

In a second exemplary embodiment, a computer screen filter, e.g. a 3M™computer screen filter, may be used as a non-refractive mask in front ofthe film in the film back. In one embodiment, the computer screen filtercontains about 14 black lines per mm, and the lines are sandwichedbetween transparent plastic material 0.2 mm thick. As a result, theF/number of the mask is approximately 3. FIG. 13 shows a Contax™ 645camera, and the film back with a 3M™ computer screen filter attached tothe window just in front of the film, according to one embodiment. Usingthis embodiment, a high-resolution radiance image of 14 samples/mm maybe captured, where each sample contains complete angular information.

Results obtained with the second exemplary embodiment of anon-refractive screen mask are shown herein, but note that the resultsfrom the first exemplary embodiment of a non-refractive screen mask aresimilar.

A sequence of parallax movies, which are generated from picturescaptured by the above exemplary internal mask-based radiance camera atdifferent apertures, may be used to illustrate that the optimal F/numberexemplary mask-based radiance camera is approximately 5.6. This value isslightly higher than the expected 3 or 4. Possible reasons are therefractive index of the plastic material, which increases optical path,and possible micro-spacing between the film and the 3M™ filter due tomechanical imperfection/dust.

FIG. 14 shows two stereo views generated, using a frequency domainmultiplexing method as illustrated in FIG. 8, from a radiance imagetaken using the exemplary mask-based radiance camera with the mask atF/5.6. Selected areas show detail in which it is easy to spot parallax.Note that, as in FIGS. 12 a and 12 b, the left and right images areswitched.

External Mask-Based Radiance Cameras

In the section titled Placing the array in front of the camera, it wasdemonstrated that a non-refractive mask or screen in front of thephotosensor or film may be replaced with a non-refractive mask, e.g. anet or screen, array or grid of pinholes, etc., in front of the maincamera lens. To demonstrate the method of frequency domain multiplexingfor a radiance camera based on such an external mask, pictures may betaken with a conventional camera through a net, mesh, or screen in frontof the camera (see mask 302A of FIG. 16 to view what such a net, mesh orscreen may look like). For the demonstration, a conventional camera withan 80 mm lens and a digital back, without any modifications to thecamera, may be used. For the demonstration, the mesh is placedapproximately 2 meters (m) from the camera, and the camera is focused ona plane about 10 centimeters (cm) behind the net or mesh. With thisapparatus, the cover glass problem of the mask-based radiance camerasdescribed above may be overcome. Note that the above-described apparatusis exemplary, and not intended to be limiting. Embodiments of anexternal mask-based radiance camera 300 that employs similar principlesdemonstrated via the above exemplary apparatus are illustrated in anddescribed in reference to FIG. 19.

By differentiating the lens equation:

${\frac{1}{a} + \frac{1}{b}} = \frac{1}{f}$the following is obtained:

$\frac{da}{a^{2}} = {- \frac{db}{b^{2}}}$

Therefore, moving the focus by da=10 cm away from the net or meshproduces a movement of:

${{- {da}}\frac{b^{2}}{a^{2}}} = {0.16\mspace{11mu}{mm}}$away from the photosensor surface. At the same time, the image of the 2mm grid of the net or mesh has been reduced linearly to 0.08 mm, whichgives an F/number of about 3, and high resolution.

FIG. 15 shows a picture taken through a net, or mesh, using theapparatus described above. The Figure shows an image taken through amesh with a conventional camera at F/number 4. FIG. 16 shows two stereoviews from the radiance generated from the picture shown in FIG. 15. Theleft and right images are switched. The two stereo views of the scenemay be reconstructed using a method of demultiplexing in the frequencydomain as illustrated in FIG. 8.

FIGS. 17 and 18 illustrate exemplary non-refractive masks, according toembodiments. With appropriate physical adaptations for mounting orotherwise attaching the masks in or to the cameras, the exemplary masksmay, be used as internal masks, e.g. placed in front of the photosensor,for example in a film-back camera as previously described, or asexternal masks placed in front of the main camera lens, for example inan external mask-based radiance camera as illustrated in FIG. 19. Themasks are non-refractive; that is, while the masks may act to modulateand/or attenuate the light, the masks do not act to bend the light rays.It is important to note that the exemplary non-refractive masks are notlimited to sinusoidal (e.g., cosine or sine) masks. In other words, anyperiodic mask may be used in mask-based radiance cameras as describedherein.

FIG. 17 shows examples of net- or mesh-like, non-refractive masks. Mask302A illustrates a rectangular mesh-like mask. Mask 302B illustrates acircular mesh-like mask 302B. A mesh, which also may be referred to as anet or screen, may include horizontally and vertically arranged opaquelinear elements or grid lines, which collectively form a grid thatmodulates, but does not refract, light as the light passes through thegrid. Generally, the opaque grid lines may be equally spaced in the twodimensions. Thus, the opaque grid lines act to form or define rows andcolumns of periodically spaced transparent (i.e., through which lightmay pass), non-refractive openings. In this example, the openings aresquare; however, in some embodiments, the openings may be rectangularbut not square. In some embodiments, a mesh mask may include onlyhorizontal or vertical lines, as illustrated in mask 302C.

FIG. 18 shows examples of some other types of non-refractive masks 302that, like the masks illustrated in FIG. 17, may be used as internal orexternal masks. Mask 302D illustrates an exemplary circular mask thatincludes transparent circular openings, through which light may pass, inan opaque medium or surface. The circular openings in this example areperiodically spaced, and arranged in horizontal rows and verticalcolumns. Other geometric shapes than circles may be used for theopenings in other embodiments, e.g. squares, hexagons, rectangles, etc.Mask 302E illustrates an exemplary circular mask that is composed of agrid of pinholes in an opaque medium or surface. The pinholes, which mayalso be referred to as openings, may typically be, but are notnecessarily, circular. Like the circular openings of mask 302D, thepinholes in this example are periodically spaced, and arranged inhorizontal rows and vertical columns. Note that the pinhole mask 302Eappears similar to mask 302D. However, the use of the term “pinhole”indicates that the size of the openings is very small, as in the opticalnotion of a “pinhole camera”; very small openings, or pinholes, haveoptical effects that are not produced, or not produced to the samedegree, by larger openings. In other words, a mask with very smallopenings may be referred to as a pinhole mask, while a mask with largeropenings, such as mask 302D, is not technically a pinhole mask. Mask302F illustrates another pinhole mask, this one rectangular instead ofcircular, and in which the pinholes are aligned differently than thepinholes in mask 302E.

In various embodiments, the opaque grid lines of the masks 302illustrated in FIG. 17, or the opaque surface or medium through whichthere are openings of the masks 302 illustrated in FIG. 18, may becomposed of a metal, a paint, an alloy, a plastic, a composite material,or any other suitable opaque substance, composition or material capableof being arranged, affixed or applied to form the linear, opaqueelements of a grid, or an opaque surface through which openings may beprovided, for use in an optical device. In some embodiments, the grid orsurface with openings may be affixed to, painted on, or otherwiseattached to a surface of a non-refracting, transparent sheet of glass.In other embodiments, the grid or surface with openings may besandwiched between two non-refracting, transparent sheets of glass.Other non-refracting, transparent materials than glass may be used. Oneskilled in the art will recognize that other materials and methods ofmanufacturing such masks are possible.

Note that the openings in masks 302, including but not limited to theexemplary masks illustrated in FIGS. 17 and 18, may be variably spacedwithout restriction on the spacing other than periodicity. That is,while the openings are arranged periodically, the distribution of theopenings in the masks 302 is not limited to, for example, the cosine, orinteger multiples of the cosine. In other words, while sinusoidal maskssuch as cosine masks may be used in embodiments, periodic masks otherthan sinusoidal masks may also be used in embodiments.

In some embodiments of an external mask-based camera such as camera 300of FIG. 19, a mask 302 may be integrated with, or alternatively may becoupled to and decoupled from, an attachment, e.g. a tube. Theattachment, in turn, may be coupled to and decoupled from a camera body.Alternatively, the mask 302 may be integrated with the attachment. Asyet another alternative, the mask 302 may be integrated with the camerabody, in front of the main or objective lens of the camera. In oneembodiment, the mask 302, when integrated with or coupled to a camera,is positioned so that the horizontal and vertical grid lines, or rowsand columns of openings, are horizontal and vertical with respect to thecamera, i.e. the photosensor, so that the horizontal grid lines (or rowsof openings) are parallel to the horizontal axis of the photosensor, andthe vertical grid lines (or columns of openings) are parallel to thevertical axis of the photosensor.

The exemplary masks of FIGS. 17 and 18 are not intended to be limiting;other geometric shapes may be used for masks 302, the number, thicknessand spacing of the opaque elements or grid lines in mesh-like masks suchas masks 302A, 302B, and 302C may vary, and as mentioned above, thesize, shape, and spacing of the openings in other types of masks such asmasks 302D, 302E and 302F may vary.

Embodiments of a radiance camera based on an external, non-refractivemask located in front of the main or objective camera lens, rather thanbetween the main lens and the photosensor or film, are described. FIG.19 illustrates an exemplary radiance camera with an external mask,according to one embodiment. External mask radiance camera 300 mayinclude a camera body 310. Various types of cameras may be used in someembodiments, including both film-based and digital cameras, andstandard, medium or large-format cameras. Thus, photosensor 330 may beconventional film or a device for digitally capturing light, for examplea CCD, and photosensor 330 may be integrated into camera body 310 ormounted to camera body 310 via a film back such as in the camera shownin FIG. 13. Main (objective) lens 320 may be any of a variety of typesof lenses, including lenses with different focal lengths or otheroptical characteristics, and may be integrated into camera body 310 ormounted to camera body 310 via an external lens attachment.

A non-refractive mask 302, such as exemplary mesh-like masks 302Athrough 302C illustrated in FIG. 17, or exemplary masks 302D through302F illustrated in FIG. 18, may be integrated with camera body 310 infront of the main lens 320, or alternatively attachable to camera body310 or to an external attachment 304, with mask 302 positioned in frontof the main lens 320 so that light from a scene to be photographedarrives at the main lens 320 after passing through the mask 302. Themask 302 is a non-refractive element, and as such modulates and/orattenuates the incoming light rays but does not bend them. The mask 302is not limited to sinusoidal masks such as cosine masks or sine masks;any arbitrary periodic mask may be used. In one embodiment, the mask 302may be mounted in or integrated with a mask attachment 304. Maskattachment 304 may be integrated with camera body 310, or alternativelymay be coupled to and decoupled from camera body 310 in front of mainlens 320. Note that the illustrated shape and size, including thelength, of mask attachment 304 is exemplary, and not intended to belimiting. Furthermore, the sizes and spacing of the mask 302, maskattachment 304, main lens 320, camera body 310, and photosensor 330 areexemplary and not intended to be limiting. In other words, externalmask-based radiance camera 300 is not necessarily drawn to scale.

In one embodiment, the main lens 320 may be focused on a plane 322 justbehind the mask 302, between the mask 302 and the main lens 320. Lightfrom plane 322 is refracted by main lens 320 onto photosensor 330, whichmay in turn operate to capture a radiance image of the scene, e.g. whena shutter of the camera 300 is triggered. An exemplary radiance imagecaptured with a mask (in this example, a net- or mesh-like mask) locatedin front of the main camera lens is shown in FIG. 15.

The angular information of radiance images captured with embodiments ofexternal mask radiance camera 300 may be demultiplexed using anembodiment of the frequency domain demultiplexing method described inFIG. 8 to generate multiple views of a scene. The frequency domaindemultiplexing method may be implemented in an embodiment of a frequencydomain demultiplexing module as illustrated in FIG. 10.

In general, embodiments of an external mask radiance camera 300 asdescribed herein may include, in addition to the above-describedelements, any other type of elements and features commonly found indigital cameras or other cameras including but not limited toconventional light-field and plenoptic cameras and medium- orlarge-format film cameras, and may also include additional elements andfeatures not generally found in conventional cameras. Camera 300 mayinclude a shutter, which may be located in front of or behind objectivelens 320. Camera 300 may include one or more processors, a power supplyor power source, such as one or more replaceable or rechargeablebatteries. Camera 300 may include a memory storage device or system forstoring captured images or other information such as software. In oneembodiment, the memory system may be or may include aremovable/swappable storage device such as a memory stick. Camera 300may include a screen (e.g., an LCD screen) for viewing scenes in frontof the camera prior to capture and/or for viewing previously capturedand/or rendered images. The screen may also be used to display one ormore menus or other information to the user. Camera 300 may include oneor more I/O interfaces, such as FireWire or Universal Serial Bus (USB)interfaces, for transferring information, e.g. captured images, softwareupdates, and so on, to and from external devices such as computersystems or even other cameras. Camera 300 may include a shutter releasethat is activated to capture a radiance image of a subject or scene.Camera 300 may include one or more manual and/or automatic controls, forexample controls for controlling optical aspects of the camera such asshutter speed, aperture, and the location of focal plane 322 of the mainlens 330, one or more controls for viewing and otherwise managing andmanipulating captured images stored in a memory on the camera, etc.

FIG. 20 illustrates a method of capturing a radiance image with anexternal mask-based radiance camera, according to one embodiment. Theexternal mask-based radiance camera multiplexes radiance in thefrequency domain by optically mixing different spatial and angularfrequency components of the light received from a scene, and capturesthe radiance information at a photosensor. As illustrated at 400, lightfrom a scene may be received at a mask 302. The mask 302 is anon-refractive element, and modulates and/or attenuates the incominglight rays but does not bend them. Light that passes through the mask302 is received at the main lens 320 of a camera 300, as indicated at402. The main lens 320 may be focused on a plane 322 between the mask302 and the main lens 320, with the plane 322 proximate to the mask 302.The received light may be refracted by the main lens 320 to aphotosensor 330 of the camera 300, as indicated at 404. The photosensor330 may capture the received light as a radiance image of the scene, asindicated at 406. As indicated at 408, the angular information in thecaptured radiance image may be demultiplexed using an embodiment of thefrequency domain demultiplexing method described in FIG. 8 to generatemultiple views of the scene. The frequency domain demultiplexing methodmay be implemented in an embodiment of a frequency domain demultiplexingmodule as illustrated in FIG. 10.

In some embodiments, the captured radiance image and/or the multipleviews generated by the frequency domain demultiplexing method may bestored to a memory medium or memory device. Note that, if the radianceimage was originally captured to film, i.e. if the camera is a filmcamera, the radiance image may be digitized from the film or from aphotograph produced from the film, for example using a film negative orphotograph scanner, to generate a digital version of the radiance imagethat may be stored to a memory medium and/or processed by the frequencydomain demultiplexing method of FIG. 8.

FIG. 21 illustrates an exemplary embodiment of an internal mask-basedradiance camera based on a medium- or large-format film camera with afilm back. In conjunction with current high-resolution scanners used todigitize captured images from negatives or prints, large-format filmcamera embodiments may be capable of up to 1 gigapixel, or even higher,resolution for the flat or light-field representation of the 4D radiance(the raw radiance image). FIG. 13 shows an exemplary embodiment of aconventional medium-format film camera and a film back, with a computerscreen filter, used as a mask, attached to the window just in front ofthe film. Another exemplary embodiment may, for example, be implementedin large-format film camera using a 135 mm objective lens 530 and 4×5format film as the “photosensor” (in medium- and large-format cameras,single negatives of film are generally placed in a film holder 502 orcartridge that can be inserted into and removed from the camera body).Other objective lenses and/or other medium or large film formats, forexample 8×10 format film, may be used in various embodiments.

Radiance camera 500 includes a mask 406. Mask 406 is a non-refractiveoptical element, and as such modulates and/or attenuates light rays butdoes not bend them. Mask 506 may be a mesh-like mask such as exemplarymesh-like masks 302A through 302C illustrated in FIG. 17, or anothertype of mask such as exemplary masks 302D through 302F illustrated inFIG. 18. Note, however, that the mask 506 will generally be rectangular,and sized to match the format of the film camera. The mask 506 is notlimited to sinusoidal masks such as cosine masks or sine masks; anyarbitrary periodic mask may be used.

In one embodiment, a mechanism inside a film holder 502 of thelarge-format film camera holds the mask 506 so that the flat side of theglass base of the mask 506 is pressed against the film and the opaquesurface of the mask 506 (the surface of mask 506 on which the opaquesurface or medium is painted, attached, etc., with openings that are thetransparent portion of the mask) is away from the film. In oneembodiment, the thickness of the mask 506 is such that, when placedagainst the film, the opaque surface of the mask 506, and the openingstherein, is at a distance f (equivalent to the focal length of the mask506) from the film. Other configurations of masks 506 are possible, andthe configuration of the medium- or large-format film camera with a filmback 502 makes it possible to easily change configurations of masks bysimply using a different mask 506. In one embodiment, microsheets 504 ofglass may be used in the assembly as spacers or shims between the mask506 and the film in film holder 502 to increase the distance from themask 506 and the film to allow f (equivalent to the focal length of themask 506) to be changed, for example to match a changed F/number formain lens 530. An exemplary thickness of a microsheet 504 that may beused is 0.23 mm. Additional microsheets 404 may be added to provideadditional spacing. The ability to insert or remove microsheet glass504, to insert or remove one or more microsheets 504 of glass, and theavailability of microsheet glass 504 in different, precisely knownthicknesses may provide spacing in a rigorously controlled manner. Insome embodiments, other mechanisms than microsheet glass 504 may be usedas spacers between the mask 506 and film holder 502 to adjust thedistance between the mask 506 and film holder 502.

As illustrated in FIG. 21, in one embodiment, the film holder 502 andmask 406 may be coupled to create assembly 510. One or more microsheets504 may optionally be inserted between the film holder 502 and mask 506to provide additional spacing as necessary or desired. The assembly 510may then be inserted into the large-format film camera. The combinationof the large-format film camera and the assembly 510 effectively forms aradiance camera 500. Radiance camera 500 may then be used to capture aradiance image of a scene on the film in film holder 502. The assembly510 may then be removed from the camera 500, disassembled, and the filmmay be appropriately processed. The film negative and/or a print of theradiance image may then be digitized, for example using ahigh-resolution scanner or a device that generates digital images fromnegatives. The digitized radiance image may be stored to a storagedevice, such as a disk drive, DVD, CD, etc. The digitized radiance imagemay be demultiplexed according to the frequency domain demultiplexingmethod, implemented in a frequency domain demultiplexing moduleexecuting on a computer system.

Exemplary System

Various components of embodiments of a method for demultiplexingcaptured radiance in the frequency domain, as described herein, may beexecuted on one or more computer systems, which may interact withvarious other devices. One such computer system is illustrated by FIG.22. In the illustrated embodiment, computer system 700 includes one ormore processors 710 coupled to a system memory 720 via an input/output(I/O) interface 730. Computer system 700 further includes a networkinterface 740 coupled to I/O interface 730, and one or more input/outputdevices 750, such as cursor control device 760, keyboard 770, audiodevice 790, and display(s) 780. In some embodiments, it is contemplatedthat embodiments may be implemented using a single instance of computersystem 700, while in other embodiments multiple such systems, ormultiple nodes making up computer system 700, may be configured to hostdifferent portions or instances of embodiments. For example, in oneembodiment some elements may be implemented via one or more nodes ofcomputer system 700 that are distinct from those nodes implementingother elements.

In various embodiments, computer system 700 may be a uniprocessor systemincluding one processor 710, or a multiprocessor system includingseveral processors 710 (e.g., two, four, eight, or another suitablenumber). Processors 710 may be any suitable processor capable ofexecuting instructions. For example, in various embodiments, processors710 may be general-purpose or embedded processors implementing any of avariety of instruction set architectures (ISAs), such as the x86,PowerPC, SPARC, or MIPS ISAs, or any other suitable ISA. Inmultiprocessor systems, each of processors 710 may commonly, but notnecessarily, implement the same ISA.

System memory 720 may be configured to store program instructions and/ordata accessible by processor 710. In various embodiments, system memory720 may be implemented using any suitable memory technology, such asstatic random access memory (SRAM), synchronous dynamic RAM (SDRAM),nonvolatile/Flash-type memory, or any other type of memory. In theillustrated embodiment, program instructions and data implementingdesired functions, such as those described above for a method fordemultiplexing radiance in the frequency domain, are shown stored withinsystem memory 720 as program instructions 725 and data storage 735,respectively. In other embodiments, program instructions and/or data maybe received, sent or stored upon different types of computer-accessiblemedia or on similar media separate from system memory 720 or computersystem 700. Generally speaking, a computer-accessible medium may includestorage media or memory media such as magnetic or optical media, e.g.,disk or CD/DVD-ROM coupled to computer system 700 via I/O interface 730.Program instructions and data stored via a computer-accessible mediummay be transmitted by transmission media or signals such as electrical,electromagnetic, or digital signals, which may be conveyed via acommunication medium such as a network and/or a wireless link, such asmay be implemented via network interface 740.

In one embodiment, I/O interface 730 may be configured to coordinate I/Otraffic between processor 710, system memory 720, and any peripheraldevices in the device, including network interface 740 or otherperipheral interfaces, such as input/output devices 750. In someembodiments, I/O interface 730 may perform any necessary protocol,timing or other data transformations to convert data signals from onecomponent (e.g., system memory 720) into a format suitable for use byanother component (e.g., processor 710). In some embodiments, I/Ointerface 730 may include support for devices attached through varioustypes of peripheral buses, such as a variant of the Peripheral ComponentInterconnect (PCI) bus standard or the Universal Serial Bus (USB)standard, for example. In some embodiments, the function of I/Ointerface 730 may be split into two or more separate components, such asa north bridge and a south bridge, for example. In addition, in someembodiments some or all of the functionality of I/O interface 730, suchas an interface to system memory 720, may be incorporated directly intoprocessor 710.

Network interface 740 may be configured to allow data to be exchangedbetween computer system 700 and other devices attached to a network,such as other computer systems, or between nodes of computer system 700.In various embodiments, network interface 740 may support communicationvia wired or wireless general data networks, such as any suitable typeof Ethernet network, for example; via telecommunications/telephonynetworks such as analog voice networks or digital fiber communicationsnetworks; via storage area networks such as Fibre Channel SANs, or viaany other suitable type of network and/or protocol.

Input/output devices 750 may, in some embodiments, include one or moredisplay terminals, keyboards, keypads, touchpads, scanning devices,voice or optical recognition devices, or any other devices suitable forentering or retrieving data by one or more computer system 700. Multipleinput/output devices 750 may be present in computer system 700 or may bedistributed on various nodes of computer system 700. In someembodiments, similar input/output devices may be separate from computersystem 700 and may interact with one or more nodes of computer system700 through a wired or wireless connection, such as over networkinterface 740.

As shown in FIG. 22, memory 720 may include program instructions 725,configured to implement embodiments of a method for demultiplexingradiance in the frequency domain as described herein, and data storage735, comprising various data accessible by program instructions 725. Inone embodiment, program instructions 725 may include software elementsof a method for demultiplexing radiance in the frequency domain asillustrated in the above Figures. Data storage 735 may include data thatmay be used in embodiments. In other embodiments, other or differentsoftware elements and data may be included.

Those skilled in the art will appreciate that computer system 700 ismerely illustrative and is not intended to limit the scope of a methodfor demultiplexing radiance in the frequency domain as described herein.In particular, the computer system and devices may include anycombination of hardware or software that can perform the indicatedfunctions, including computers, network devices, internet appliances,PDAs, wireless phones, pagers, etc. Computer system 700 may also beconnected to other devices that are not illustrated, or instead mayoperate as a stand-alone system. In addition, the functionality providedby the illustrated components may in some embodiments be combined infewer components or distributed in additional components. Similarly, insome embodiments, the functionality of some of the illustratedcomponents may not be provided and/or other additional functionality maybe available.

Those skilled in the art will also appreciate that, while various itemsare illustrated as being stored in memory or on storage while beingused, these items or portions of them may be transferred between memoryand other storage devices for purposes of memory management and dataintegrity. Alternatively, in other embodiments some or all of thesoftware components may execute in memory on another device andcommunicate with the illustrated computer system via inter-computercommunication. Some or all of the system components or data structuresmay also be stored (e.g., as instructions or structured data) on acomputer-accessible medium or a portable article to be read by anappropriate drive, various examples of which are described above. Insome embodiments, instructions stored on a computer-accessible mediumseparate from computer system 700 may be transmitted to computer system700 via transmission media or signals such as electrical,electromagnetic, or digital signals, conveyed via a communication mediumsuch as a network and/or a wireless link. Various embodiments mayfurther include receiving, sending or storing instructions and/or dataimplemented in accordance with the foregoing description upon acomputer-accessible medium. Accordingly, the present invention may bepracticed with other computer system configurations.

CONCLUSION

Various embodiments may further include receiving, sending or storinginstructions and/or data implemented in accordance with the foregoingdescription upon a computer-accessible medium. Generally speaking, acomputer-accessible medium may include storage media or memory mediasuch as magnetic or optical media, e.g., disk or DVD/CD-ROM, volatile ornon-volatile media such as RAM (e.g. SDRAM, DDR, RDRAM, SRAM, etc.),ROM, etc. A computer-accessible medium may also include transmissionmedia or signals such as electrical, electromagnetic, or digitalsignals, conveyed via a communication medium such as network and/or awireless link.

The various methods as illustrated in the Figures and described hereinrepresent exemplary embodiments of methods. The methods may beimplemented in software, hardware, or a combination thereof. The orderof method may be changed, and various elements may be added, reordered,combined, omitted, modified, etc.

Various modifications and changes may be made as would be obvious to aperson skilled in the art having the benefit of this disclosure. It isintended that the invention embrace all such modifications and changesand, accordingly, the above description to be regarded in anillustrative rather than a restrictive sense.

What is claimed is:
 1. An apparatus, comprising: a camera comprising anobjective lens, wherein the objective lens is configured to refractlight from a scene located in front of the camera to form an image ofthe scene at a focal plane of the objective lens; a film holderconfigured to hold a film and to be inserted into and removed from thecamera; and a non-refractive periodic mask configured to be placed inthe film holder against the film such that the mask is between the filmand the objective lens of the camera and at the focal plane of thecamera when the film holder is inserted into the camera, wherein themask comprises an opaque medium with periodically spaced transparentopenings on one surface positioned away from the film, and wherein theopposite surface of the mask is configured to be positioned next to thefilm; wherein the apparatus is configured to multiplex radiance in thefrequency domain by optically mixing different spatial and angularfrequency components of the light received from the scene and to capturethe multiplexed radiance on the film.
 2. The apparatus as recited inclaim 1, further comprising one or more spacers configured to be placedbetween the mask and the film in the film holder to adjust the distancebetween the mask and the film.
 3. The apparatus as recited in claim 2,wherein the spacers are sheets of clear glass.
 4. The apparatus asrecited in claim 1, wherein the periodic mask is a non-sinusoidalperiodic mask.
 5. The apparatus as recited in claim 1, wherein theapparatus is configured to satisfy the equation: $\frac{f}{b} = F$ whereF is the F/number of the objective lens, b is the lowest frequency inthe periodic mask, and f is the distance from the surface of the maskpositioned away from the film to the surface of the film.
 6. A camera,comprising: an objective lens, wherein the objective lens is configuredto refract light received from a scene in front of the camera onto afocal plane in the camera; a photosensor configured to capture lightprojected onto the photosensor; a non-sinusoidal periodic maskpositioned between the objective lens and the photosensor at the focalplane, wherein the mask is configured to modulate but not refract lightreceived from the objective lens as the received light passes throughthe mask and onto the photosensor; wherein the camera multiplexesradiance in the frequency domain by optically mixing different spatialand angular frequency components of the light received from the scene.7. The camera as recited in claim 6, wherein the mask comprises a gridof multiple horizontally and vertically arranged opaque linear elementsthat define horizontal rows and vertical columns of periodically spacedtransparent openings between the opaque linear elements.
 8. The cameraas recited in claim 6, wherein the mask comprises an opaque surfacethrough which there are multiple periodically spaced transparentopenings arranged in horizontal rows and vertical columns.
 9. The cameraas recited in claim 6, wherein the camera is configured to satisfy theequation: $\frac{f}{b} = F$ where F is the F/number of the objectivelens, b is the lowest frequency in the non-sinusoidal periodic mask, andf is the distance from a surface of the mask positioned away from thephotosensor to a surface of the photosensor proximate to the mask. 10.The camera as recited in claim 6, wherein the photosensor is configuredto capture a radiance image of the scene, wherein the captured radianceimage includes the optically mixed different spatial and angularfrequency components of the light received from the scene.